Convert the following problem to simplex read equation. Min. Z = 4 X_1 + 4 X_2 s
ID: 3121535 • Letter: C
Question
Convert the following problem to simplex read equation. Min. Z = 4 X_1 + 4 X_2 s.I. 3 XI_1 + 5 X_2 greaterthanorequalto 150 X_1 - 10 2 X_2 lesserthanorequalto 10 x_1, x_2 greaterthanorequalto 0 Lee Company produces Mattresses at 2 plants (A&B;). Mattresses then shipped to three warehouses (1, 2 & 3). The cost per mattress of shipping from each of the two plants to the three warehouses is as follows. The Plant A can supply 2000 mattresses per week; the plant B can supply 3000 and the week. The Warehouse 1 has a demand of 2500 mattresses per week, and the Warehouse 2 demands 1500 mattresses per week. The warehouse 3 has a demand of 1000 mattresses per week. The company wants to know the number mattresses to ship from each plant to each warehouse in order to minimize the total shipping cost. First make an initial assignment using Northwest Corner method. Then find the optimal solution using stepping-stone method. Find the shortest path from the office to the customer.Explanation / Answer
Question no. 5. To write the simplex ready equation, the steps are as follows.
1. Convert inequalities into equations by introducing slack variables in the less than or equal to constraints and surplus variables and artificial variables in the greater than or equal to constraints.
In the problem, the first constraint is 3x1 + 5x2 >= 150.
The corresponding equation is 3x1 + 5x2 - s1 + A1 = 150, Where s1 is a surplus variable and A1 is the artificial variable.
The second constraint is x1 - 2x2 <= 10
The corresponding equation is x1 - 2x2 + s2 = 10, Where s2 is a slack variable.
The next step is to rewrite the objective function by incorporating the slack, surplus and artificial variables.
Therefore the objective function is Min Z = 4x1 + 4x2 + 0s1 +0s2+ MA1.
Hence the simplex ready equation is
Min Z = 4x1 + 4x2 + 0s1 +0s2+ MA1.
s.t.
3x1 + 5x2 - s1 + A1 = 150,
x1 - 2x2 + s2 = 10,
x1, x2, s1, s2, A1 >= 0